Despite the Prime Minister supposedly securing "legally binding" changes, the DUP has not openly confirmed its support for Mrs May's deal as of yet.
Scrambling to plot an orderly path out of the Brexit maze just days before the United Kingdom is due to leave on March 29, May rushed to Strasbourg to agree additional assurances with European Commission President Jean-Claude Juncker. Citing officials in May's office, Sky News also reported she would travel to Strasbourg.
If Tuesday's meaningful vote to approve May's current Brexit deal fails, a vote will be held on Wednesday to determine if Britain should leave the European Union without a deal.
While May has said she wants to stay on in power to deliver a domestic legacy, the votes in Parliament this week might determine the length of her remaining time in Downing Street.
"We were going to have to start facing these choices this summer anyway under the prime minister's deal".
Pro-Brexit U.K. lawmakers said they would read the fine print and wait for the judgment of Britain's attorney general before deciding how to vote on Tuesday.
That's unlikely. There are a few hard-core "Brexiteer" members of Parliament in May's Conservative Party who support leaving the European Union with no deal, and a recent poll showed a majority of the party's rank-and-file members agree.
Senior Conservative lawmakers advised the prime minister in phone conversations that she should delay the vote and put forward a motion describing a divorce agreement that would finally heal divisions over the issue within May's own party, according to The Times.
"Discussions are ongoing between ourselves and the EU", May's spokesman had earlier told reporters, insisting that Tuesday's vote would take place as planned.
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The UK has spent almost three years trying to negotiate a divorce from the European Union, following the June 2016 referendum that resulted in the surprise victory of those in favor of Brexit.
The EU is unwilling to reopen the 585-page Brexit agreement, though it has offered what it says are legally binding promises that the backstop will not be permanent.
Labour MPs pressing for a "common market 2.0" kind of Brexit said they were conducting intensive shuttle diplomacy between Jeremy Corbyn's team and Conservative MPs who might be ready to back the idea.
May has said if she loses the vote on Tuesday, there will be further votes on Wednesday on whether the United Kingdom should leave with no-deal and on Thursday on whether they should seek an extension to the Article 50 withdrawal process.
After MPs gave her a mandate to go back to Brussels and renegotiate the deal, May gave herself until March 12 at the latest to bring a revised deal back to Parliament.
May has already survived a leadership challenge from within the Conservative Party, which means there can not be another one before December.
With a number of Labour MPs against a second vote, it remains unclear whether it would find a majority in Parliament.
"What happens is the British people who voted for this. will see a government walking away, a parliament walking away from a question that they themselves put to the people", said Davis.
Lawmakers will spend several hours on Tuesday debating the prime minister's deal.